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Lie Infinity-Algebras from Lie Rinehart Pairs
[article]
2013
arXiv
pre-print
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We generalize the Schouten calculus of multivector fields to commutative Lie Rinehart pairs and define a non negatively graded Lie oo-algebra on their exterior power.
arXiv:1311.2228v2
fatcat:ju6kcz3zr5b4pglcpvv34lb4hy
Towards Homotopy Poisson-n Algebras from N-plectic Structures
[article]
2018
arXiv
pre-print
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We associate a homotopy Poisson-n algebra to any higher symplectic structure, which generalizes the common symplectic Poisson algebra of smooth functions. This provides robust n-plectic prequantum data for most approaches to quantization. UPDATE: It has been brought to my attention that the exterior product does not close on the exterior cotensors called Poisson cotensors in the present paper. Therefore the set of Poisson cotensors as presented, is not quite yet a homotopy Poisson-n algebra.
arXiv:1506.01129v2
fatcat:feuqsyv2hbfupei4pfbhcovfj4
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... ever for those Poisson cotensor that do multiply into Poisson cotensors under the exterior prodoct, the computation remains valid and interesting, nonetheless. Therefor this paper might better be seen as a hint towards homotopy Poisson-n algebras in higher symplectic geometry, rather then a finished theory.
Optimized Cortical Subdivision for Classification of Alzheimer's Disease With Cortical Thickness
[chapter]
2013
Bildverarbeitung für die Medizin 2013
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In several studies, brain atrophy measured by cortical thickness has shown to be a meaningful biomarker for Alzheimer's disease. In t.his research field, t.he level of granularity at which values are compared is an important aspect. Vertex-and voxel-based approaches can detect atrophy at a very fine scale, but are susceptible to noise from misregistrations and inter-subject differences in the population. Regional approaches are more robust to these kinds of noise, but cannot detect va.riances
doi:10.1007/978-3-642-36480-8_8
dblp:conf/bildmed/RichterM13
fatcat:hnctn6d7ejgcla5wezhohfedmq
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... a local scale. In this work , an optimized classifier is presented for a parcellation scheme that provides a trade-off between both paradigms by increasing the granularity of a regional approach. For this purpose, atlas regions are subdivided into gyral and sulcal parts at different height levels. Using two-stage feature selection, optimal gyral and sulcal subregions are determined for the fina.l classification with sparse logistic regression. The robustness was assessed on clinical data by 10fold cross-validation and by testing the prediction accuracy for unseen individuals. In every aspect, superior classification performance was observed as compared to the original parcellation scheme which can be explained by the increased locality of cortical thickness measures and the customized classification approach that reveals interacting regions.
Anisotropy of HARDI Diffusion Profiles Based on the L2-Norm
[chapter]
2011
Bildverarbeitung für die Medizin 2011
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Abs tract. The fr actional a lliso tropy (FA ) value for Diffusion Tensor Imagill g is widely Ilsed to del.crminc t.he ani sotrop~' of di fl'usioll in a given voxel. As the FA va lue is based on the tensor's eigenvectors it is not possibl e to calculate this quantity for I-IARDI dif1'tlsion profil es. III t his paper we introduce a n a nisotropy index for HARDI data that utilizes the L 2 -norm as the most na tura l notion of distance for square-integrable fun cl ions on th e two-sphere such as
doi:10.1007/978-3-642-19335-4_50
dblp:conf/bildmed/LandgrafMR11
fatcat:hzx2rfqghjhp5lywspdjcvkkxy
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... ARDI d iffu s ion profi les a nd s li.ow tha t it is the limi t of the ge neralized fr actiona l anisotropy (GFA) index. Our index is well-defin ed a nd rota tiona lly invariant a nd thus reso lves the unsat isfactory issues with the GFA index .
A Lie Infinity Algebra of Hamiltonian Forms in n-plectic Geometry
[article]
2012
arXiv
pre-print
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We propose a new definition of so called Hamiltonian forms in n-plectic geometry and show that they have a non-trivial Lie infinity-algebra structure.
arXiv:1212.4596v2
fatcat:26cuk4fj6na3pomlknqnfj2qye
Monitoring Plant Functional Diversity Using the Reflectance and Echo from Space
2020
Remote Sensing
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Plant functional diversity (FD) is an important component of biodiversity. Evidence shows that FD strongly determines ecosystem functioning and stability and also regulates various ecosystem services that underpin human well-being. Given the importance of FD, it is critical to monitor its variations in an explicit manner across space and time, a highly demanding task that cannot be resolved solely by field data. Today, high hopes are placed on satellite-based observations to complement field
doi:10.3390/rs12081248
fatcat:kba6xmxnqnbyvfixqo7kgkzs2e
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... t data. The promise is that multiscale monitoring of plant FD, ecosystem functioning, and their services is now possible at global scales in near real-time. However, non-trivial scale challenges remain to be overcome before plant ecology can capitalize on the latest advances in Earth Observation (EO). Here, we articulate the existing scale challenges in linking field and satellite data and further elaborated in detail how to address these challenges via the latest innovations in optical and radar sensor technologies and image analysis algorithms. Addressing these challenges not only requires novel remote sensing theories and algorithms but also urges more effective communication between remote sensing scientists and field ecologists to foster mutual understanding of the existing challenges. Only through a collaborative approach can we achieve the global plant functional diversity monitoring goal.
Higher symplectic structure on torsionless Lie-Rinehart pairs
[article]
2014
arXiv
pre-print
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We define an n-plectic structure as a commutative and torsionless Lie Rinehart pair, together with a distinguished cocycle from its Chevalley-Eilenberg complex. This 'n-plectic cocycle' gives rise to an extension of the Chevalley-Eilenberg complex by so called symplectic tensors. The cohomology of this extension generalizes Hamiltonian functions and vector fields to tensors and cotensors in a range of degrees, up to certain coboundaries and has the structure of a Lie oo-algebra. Finally we
arXiv:1312.7752v4
fatcat:or3m6anblna43ccgdnyw3ldrxy
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... that momentum maps appear in this context just as weak Lie oo-morphisms from an arbitrary Lie oo-algebra into the Lie oo-algebra of Hamiltonian (co)tensors.
Fast and Accurate Connectivity Analysis Between Functional Regions Based on DT-MRI
[chapter]
2006
Lecture Notes in Computer Science
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Diffusion tensor and functional MRI data provide insight into function and structure of the human brain. However, connectivity analysis between functional areas is still a challenge when using traditional fiber tracking techniques. For this reason, alternative approaches incorporating the entire tensor information have emerged. Based on previous research employing pathfinding for connectivity analysis, we present a novel search grid and an improved cost function which essentially contributes to
doi:10.1007/11866763_28
fatcat:ldvyc6khijelbhhu62ae2akeoa
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... more precise paths. Additionally, implementation aspects are considered making connectivity analysis very efficient which is crucial for surgery planning. In comparison to other algorithms, the presented technique is by far faster while providing connections of comparable quality. The clinical relevance is demonstrated by reconstructed connections between motor and sensory speech areas in patients with lesions located in between.
Intraoperative Visualization of Fiber Tracking Based Reconstruction of Language Pathways in Glioma Surgery
2012
Neurosurgery
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BACKGROUND: For neuroepithelial tumors, the surgical goal is maximum resection with preservation of neurological function. This is contributed to by intraoperative magnetic resonance imaging (iMRI) combined with multimodal navigation. OBJECTIVE: We evaluated the contribution of diffusion tensor imaging (DTI)-based fiber tracking of language pathways with 2 different algorithms (tensor deflection, connectivity analysis [CA]) integrated in the navigation on the surgical outcome. METHODS: We
doi:10.1227/neu.0b013e318237a807
pmid:21946508
fatcat:ujhciycxmvh7hi76gf3adztdne
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... ted 32 patients with neuroepithelial tumors who underwent surgery with DTI-based fiber tracking of language pathways integrated in neuronavigation. The tensor deflection algorithm was routinely used and its results intraoperatively displayed in all cases. The CA algorithm was furthermore evaluated in 23 cases. Volumetric assessment was performed in pre-and intraoperative MR images. To evaluate the benefit of fiber tractography, language deficits were evaluated pre-and postoperatively and compared with the volumetric analysis. RESULTS: Final gross-total resection was performed in 40.6% of patients. Absolute tumor volume was reduced from 55.33 6 63.77 cm 3 to 20.61 6 21.67 cm 3 in first iMRI resection control, to finally 11.56 6 21.92 cm 3 (P , .01). Fiber tracking of the 2 algorithms showed a deviation of the displayed 3D objects by ,5 mm. In long-term followup only 1 patient (3.1%) had a persistent language deficit. CONCLUSION: Intraoperative visualization of language-related cortical areas and the connecting pathways with DTI-based fiber tracking can be successfully performed and integrated in the navigation system. In a setting of intraoperative high-field MRI this contributes to maximum tumor resection with low postoperative morbidity.
Evaluation of Diffusion-Tensor Imaging-Based Global Search and Tractography for Tumor Surgery Close to the Language System
2013
PLoS ONE
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Pre-operative planning and intra-operative guidance in neurosurgery require detailed information about the location of functional areas and their anatomo-functional connectivity. In particular, regarding the language system, post-operative deficits such as aphasia can be avoided. By combining functional magnetic resonance imaging and diffusion tensor imaging, the connectivity between functional areas can be reconstructed by tractography techniques that need to cope with limitations such as
doi:10.1371/journal.pone.0050132
pmid:23308093
pmcid:PMC3538752
fatcat:mg3c4lej4ral7lz3453ci4crje
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... ed resolution and low anisotropic diffusion close to functional areas. Tumors pose particular challenges because of edema, displacement effects on brain tissue and infiltration of white matter. Under these conditions, standard fiber tracking methods reconstruct pathways of insufficient quality. Therefore, robust global or probabilistic approaches are required. In this study, two commonly used standard fiber tracking algorithms, streamline propagation and tensor deflection, were compared with a previously published global search, Gibbs tracking and a connection-oriented probabilistic tractography approach. All methods were applied to reconstruct neuronal pathways of the language system of patients undergoing brain tumor surgery, and control subjects. Connections between Broca and Wernicke areas via the arcuate fasciculus (AF) and the inferior fronto-occipital fasciculus (IFOF) were validated by a clinical expert to ensure anatomical feasibility, and compared using distance-and diffusion-based similarity metrics to evaluate their agreement on pathway locations. For both patients and controls, a strong agreement between all methods was observed regarding the location of the AF. In case of the IFOF however, standard fiber tracking and Gibbs tracking predominantly identified the inferior longitudinal fasciculus that plays a secondary role in semantic language processing. In contrast, global search resolved connections in almost every case via the IFOF which could be confirmed by probabilistic fiber tracking. The results show that regarding the language system, our global search is superior to clinically applied conventional fiber tracking strategies with results similar to time-consuming global or probabilistic approaches.
Current status, uncertainty and future needs in soil organic carbon monitoring
2014
Science of the Total Environment
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, 2007; Richter and Yaalon, 2012) . ...
More than 100 archives exist and many have been established within the past 60 years (Richter et al., 2007; Richter and Yaalon, 2012) . ...
doi:10.1016/j.scitotenv.2013.08.026
pmid:24041605
fatcat:cut4ehug4zcdnggqnphiktg3s4
Data Products, Quality and Validation of the DLR Earth Sensing Imaging Spectrometer (DESIS)
2019
Sensors
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The validation results of the WV retrieval algorithm, using the water absorption region of 820 nm, are consistent with the APDA algorithm validation performed by Richter and Schlapfer [128] , who estimated ...
doi:10.3390/s19204471
fatcat:xzwufpdbszetnidpcsmoweevn4
Data Validation of the DLR Earth Sensing Imaging Spectrometer DESIS
2020
IGARSS 2020 - 2020 IEEE International Geoscience and Remote Sensing Symposium
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Imaging spectrometry provides densely sampled and finely structured spectral information for each image pixel over large areas, enabling the characterization of materials on the Earth's surface by measuring and analyzing quantitative parameters allowing the user to identify and characterize Earth surface materials such as minerals in rocks and soils, vegetation types and stress indicators, and water constituents. The recently launched DLR Earth Sensing Imaging Spectrometer (DESIS) installed on
doi:10.1109/igarss39084.2020.9323367
fatcat:zl3gexsjhjgtpo4sdhdlaxmzei
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... he International Space Station (ISS) closes the long-term gap of sparsely available spaceborne imaging spectrometry data and will be part of the upcoming fleet of such new instruments in orbit. DESIS measures in the spectral range from 400 and 1000 nm with a spectral sampling distance of 2.55 nm and a Full Width Half Maximum (FWHM) of about 3.5 nm. The various DESIS data products available for users are described with the focus on specific processing steps. A summary of the data quality results are given. The product validation studies show that top-of-atmosphere radiance, geometrically corrected, and bottom-of-atmosphere reflectance products meet the mission requirements.
Inferring plant functional diversity from space: the potential of Sentinel-2
2019
Remote Sensing of Environment
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Plant functional diversity (FD) is an important component of biodiversity that characterizes the variability of functional traits within a community, landscape, or even large spatial scales. It can influence ecosystem processes and stability. Hence, it is important to understand how and why FD varies within and between ecosystems, along resources availability gradients and climate gradients, and across vegetation successional stages. Usually, FD is assessed through laborintensive field
doi:10.1016/j.rse.2019.111368
fatcat:oochi2pesvfnre54vecfa4baae
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... nts, while assessing FD from space may provide a way to monitor global FD changes in a consistent, time and resource efficient way. The potential of operational satellites for inferring FD, however, remains to be demonstrated. Here we studied the relationships between FD and spectral reflectance measurements taken by ESA's Sentinel-2 satellite over 117 field plots located in 6 European countries, with 46 plots having in-situ sampled leaf traits and the other 71 using traits from the TRY database. These field plots represent major European forest types, from boreal forests in Finland to Mediterranean mixed forests in Spain. Based on in-situ data collected in 2013 we computed functional dispersion (FDis), a measure of FD, using foliar and whole-plant traits of known ecological significance. These included five foliar traits: leaf nitrogen concentration (N%), leaf carbon concentration (%C), specific leaf area (SLA), leaf dry matter content (LDMC), leaf area (LA). In addition they included three whole-plant traits: tree height (H), crown cross-sectional area (CCSA), and diameter-at-breast-height (DBH). We applied partial least squares regression using Sentinel-2 surface reflectance measured in 2015 as predictive variables to model in-situ FDis measurements. We predicted, in cross-validation, 55% of the variation in the observed FDis. We also showed that the rededge, near infrared and shortwave infrared regions of Sentinel-2 are more important than the visible region for predicting FDis. An initial 30-m resolution mapping of FDis revealed large local FDis variation within each forest type. The novelty of this study is the effective integration of spaceborne and in-situ measurements at a continental scale, and hence represents a key step towards achieving rapid global biodiversity monitoring schemes.
Employing the Object Constraint Language in Model-Based Engineering
[chapter]
2013
Lecture Notes in Computer Science
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Acknowledgement The force and energy of Mark Richters, Jörn Bohling, Fabian Büttner, Mirco Kuhlmann and Lars Hamann formed USE as it stands today. Thanks! ...
doi:10.1007/978-3-642-39013-5_1
fatcat:s3g724vtgbb2nd3n5zv7l7djle
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